Download Perfect Numbers - University of Arizona Math

Perfect Numbers
A number is called "perfect" if it is equal to the sum of its proper
factors (that is, all of the factors except the number itself). For
example, 6 is a perfect number because its proper factors are 1, 2,
and 3, and 1 + 2 + 3 = 6. Try to find some other perfect numbers.
Extension: Perfect numbers are related to certain prime numbers
called Mersenne primes. A Mersenne prime is a prime number
that can be written as 2p - 1, where p is some other prime number.
For example, when p = 2, then 22 - 1 = 4 - 1 = 3, so 3 is a
Mersenne prime. Every perfect number that has been discovered
so far has a Mersenne prime as one of its factors. Can you find a
pattern or formula for the other factor? Once you find the pattern,
use it to calculate the first four perfect numbers.